The trilemma among CO2 emissions, energy use, and economic growth in Russia

This paper examines the relationship among CO2 emissions, energy use, and GDP in Russia using annual data ranging from 1990 to 2020. We first conduct time-series analyses (stationarity, structural breaks, cointegration, and causality tests). Then, we performed some Machine Learning experiments as robustness checks. Both approaches underline a bidirectional causal flow between energy use and CO2 emissions; a unidirectional link running from CO2 emissions to real GDP; and the predominance of the “neutrality hypothesis” for energy use-GDP nexus. Therefore, energy conservation measures should not adversely affect the economic growth path of the country. In the current geopolitical scenario, relevant policy implications may be derived.


Literature overview
Climate change and global warming are among the most important ongoing problems in the world, almost affecting everything adversely from economies (industrial production, agriculture, tourism, service, and other sectors) to demography (urbanization and ruralization), and hence the quality of life in general. Thus, these phenomena should be monitored by the level of CO 2 emissions. Therefore, investigating the sources and consequences of CO 2 emissions might be considered one of the most important research topics in the literature.
In this section, the relevant literature is evaluated in three different groups. Since one of the most important factors causing global warming is CO 2 emissions due to energy use, the first group consists of papers investigating the relationship between energy consumption and CO 2 emissions. Many seminal types of research have analyzed the nexus between energy consumption and the environment (Soytas and Sari 34 ; Magazzino 35,36 ; Zoundi 37 ; Bilgili et al. 38 ).
According to Table 1, the related research can be classified into, based on their samples, (a) single-country studies ( 48 ; Kuşkaya 49 ; Ozgur et al. 50 ; Apergis et al. 51 ; Kartal et al. 52 ; Kuşkaya et al. 53 ; Mukhtarov et al. 54 ) or (b) multi-country studies (Apergis et al. 55 ;Zoundi 37 ; Belaïd and Zrelli 56 ; Chontanawat 57 ; Saidi and Omri 58 ; Adebayo et al. 59 ). It is seen that auto-regressive distributed lags (ARDL), vector error correction model (VECM), and Granger causality (GC) analyses are conducted mostly in studies for a single country as seen in Table 1. In most of the papers in Table 1, there is a consensus that increasing the usage of renewable energy reduces CO 2 emissions (Lin and Moubarak 39 ; Jaforullah and King 40 ; Ben Jebli and Ben Youssef 41 ; Mirzaei and Bekri 43 ; Bekhet and Othman 44 ; Ozgur et al. 50 ; Apergis et al. 51 ; Kuşkaya et al. 53 ; Mukhtarov et al. 54 ). On the other hand, according to Beşer and Beşer 42 60 claim that the use of non-renewable energy in Thailand during the 1971-2013 period would have increased CO 2 emissions. Danish et al. 61 reached similar results for Pakistan with ARDL and VECM analyses. The second group of researchers examined the relationship between energy use or consumption (EC) and economic growth (EG). The results were evaluated according to four different hypotheses: growth, conservation, feedback, and neutrality (see Table 2).
• Growth hypothesis (EC⟹EG): it states a unidirectional causality from energy use to economic growth ( 70 ; Ntanos et al. 71 ; Luqman et al. 72 ; Shahbaz et al. 73 ; Gyimah et al. 74 ; Espoir et al. 75 ; Mohammadi et al. 76 ; Simionescu 77 ). If the growth hypothesis is valid, policies to reduce energy use have negative effects on economic growth. • Conservation hypothesis (EG⟹EC): it is valid if there is a unidirectional causality from economic growth to energy usage (Sadorsky 78 ; Menyah and Wolde-Rufael 79 ; Ocal and Aslan 80 ). In this case, policies that change energy usage do not have a negative impact on economic growth. • Feedback hypothesis (EC⟺EG): it is supported if there is a bidirectional causality between energy use and economic growth (Belloumi 81 ; Pao and Fu 82 ; Acheampong et al. 7 ; Lawal 83 ; Simionescu 77 ). • Neutrality hypothesis (EC⇎EG): it implies the absence of any causal relationship between energy use and economic growth (Lee and Chang 63 ; Pao and Fu 84 ). In this situation, policies changing energy use do not affect economic growth. www.nature.com/scientificreports/ Energy is considered an engine for economic growth. However, energy has undesirable impacts on environmental degradation as it leads to pollutant emissions (Nasir and Rehman 85 ). Therefore, the third group of works consists of papers examining the relationship between economic growth and the environment (in particular, CO 2 emissions). This group presents studies investigating the validity of the Environmental Kuznets Curve (EKC). As shown in Table 3, the validity of the EKC hypothesis has been proven in most of the studies conducted in the environmental-economics literature ( 108 and Pata and Tanriover 109 do not reach results able to provide empirical support to the EKC hypothesis. Studies investigating the EKC hypothesis for time-series generally adopt ARDL and Johansen Cointegration (JC) methodologies.
After reviewing the relevant studies in the literature, one can state that Russia can be considered a reasonable and valuable choice for an applied analysis as it is one of the countries with the highest per capita GHG emissions. Moreover, it is one of the three largest oil-producing countries in the world. On the other hand, this study aims to contribute to the literature in terms of the methodology adopted. In particular, the novelty of this paper is the combination of traditional time-series analyses together with the development of ML techniques.

Methodology and data
The empirical analysis starts with the inspection of the stationarity properties of the series. We performed several recent unit root and stationarity tests. The Kapetanios and Shin 110 test is more powerful than the linear unit root tests if there are significant asymmetries. This test is an extended version of the seminal unit root test of Kapetanios et al. 111 . Kapetanios et al. 111 introduced a model for an Exponential Smooth Transition Autoregressive (ESTAR) process, developing a nonlinear test to allow the structural change to be determined internally. In addition, the Leybourne 112 Augmented Dickey-Fuller (ADF)-max unit-root test and the Elliott et al. 113 are performed. Afterwards, the Lo 114 modified rescaled range test for long-range dependence of a time-series is used, to better understand the features of our data. Then, in order to explore the (eventual) presence of a structural breaks in the dataset, we run the recent Ditzen et al. 115 test, which implements multiple tests for structural breaks in time-series and panel data models. The number and period of occurrence of structural breaks can be known or unknown. Furthermore, to examine the long-run relationship among the variables, we apply the Bayer and Hanck 116 combined cointegration approach. This test combines the results of previous cointegration approaches (Engle and Granger 117 ; Johansen 118 ; Boswijk 119 ; Banerjee et al. 120 ) and provides Fisher F statistics Hence, the technique enables us to identify the historical changes to implement the policy intervention. However, the methodology is limited to a finite time horizon and cannot predict infinite time models. In recent years, there has been a great interest in causality discovery research and its relevant areas (Spirtes and Zhang 122 ; Nogueira et al. 123 ). Identifying the individual causal relationships between economic and financial time-series is necessary to characterize the structure of causality in an economic system. Understanding this element is essential in almost all cases involving studying complex economic systems (Zaremba and Aste 124 ).
Various techniques have been proposed to investigate causal relationships in time-series. In this work, an approach to detect causality based on GC testing (Granger 125 ) is adopted, together with a nonlinear GC test. Thus, it is essential to notice that we are explicitly dealing with time-series, which can show some linear relationships; if these are nonlinear, we must also consider a nonlinear version of the test. Following Granger 125 , Hmamouche 126 , and Gkillas et al. 127 , in order to perform a linear version of the GC test, we can write: comparing this model with a second one containing the variable to be tested in the causal relationship (X).
where l is a parameter representing the lag considered. At the same time, [α 0 , …, α l ] and [β 0 , …, β l ] are the model's parameters. Finally, the residual term Z, is a white noise process. The comparison is performed by considering the predictive power of the causal factor X against the information provided only by the lags of the Y.
The number of lags is chosen to cover the relevant, informative observations of the past, which may also be pertinent considering the degree of freedom. When the lags are added, the degree of freedom decreases directly with the addition of the lags. Thus, to assess the statistical significance, an F test is utilized to examine the validity Table 3. Summary of the selected papers on the economic growth-CO 2 emissions relationship. CUP-BC continuously updated-bias corrected, CUP-FM continuously updated-fully modified, DCCE dynamic common correlated effects, FADL fourier auto-regressive distributive lags, MMQR method of moment quantile regression.  www.nature.com/scientificreports/ of the null hypothesis, which states that the series X does not Granger cause the series Y. The test can be repeated considering both the causality directions (Ye and Zhang 128  Therefore, the VARNN(p) model can be stated as a Multi-Layer Perceptron (MLP) NN model for predicting the behaviour of Y over time. According to this approach, in addition to the target variable and its lags, l lag values of the variable predictors are considered to make Y predictions.
Furthermore, an optimization algorithm based on the stochastic gradient descent algorithm is used, allowing the weights to be updated (Gkillas et al. 127 ). The VARNN(p) model can be written in this way: where φ nn refers to the network function, and Z t is the residual (Hmamouche 126 ). In our case, we have two different models to consider. Model 1 is the following: while model 2 can be written as: Here, the two network functions are represented as φ 1nn and φ 2nn using the VARNN(p) model. An F test is utilized in testing against the null hypothesis of no causality. Again, in this case, this hypothesis is that the economic variable represented by the time-series X does not cause the time-series Y. If we refuse the null hypothesis, we find evidence of causality.
In order to confirm previous results, we apply an ML unsupervised approach to evaluate the time-series similarity structure. In this way, we adopt a method known as clustering or unsupervised learning to classify data with no prior knowledge of the classes to be categorized (Liao 130 ; Aghabozorgi et al. 131 ). Therefore, clustering time-series is an unsupervised learning approach that data analysts consider to get some insights into the patterns on a dataset (Ariff et al. 132 ; Drago and Talamo 133 ).
In general, time-series clustering may be very useful in many applications and scientific areas. In this respect, a growing interest in time-series clustering grows, particularly in the search and analysis for similarities across long-term time-series in fields such as economic or financial applications. For example, time-series clustering can be used for similar group data to be easily analyzed and then used for forecasting purposes (Corona et al. 134 ; Franses and Wiemann 135 ) or portfolio optimization (Guam and Jiang 136 ; Tola et al. 137 ).
Clustering can be defined as a technique for classifying objects related to unknown classes. In this respect, time-series can be classified into different groups with no previous information about their participation in a single group (Liao 130 ; Wang et al. 138 ). On a more technical level, clusters are constructed by grouping statistical observations within a cluster with the most significant similarity between the observations inside the same group and the lowest similarity to those outside the cluster (Fu 139 ). However, a typical data clustering approach to time-series depends also on the data structure (homogeneous or not homogeneous time-series, for instance). A different approach to clustering time-series based on temporal representation was proposed by Drago and Scepi 140 and Drago et al. 141 , which is very suitable for long time-series and high-frequency data.
In this work, we have considered the time-series classified on their structure to identify their similarities in response to shocks. This way, the clustering approach explores and evaluates the data structure to make the econometric analysis more robust. Moreover, the data exploration allows us to evaluate better and interpret the econometric models' results.
It is possible, for that purpose, to consider an unsupervised ML approach to support the different results of the causality tests. In this respect, we can explore the patterns in the data, expecting that the time-series showing patterns of causality is also characterized by higher similarity. Identifying the level of similarity of the different time-series is possible to imply a measurement of the joint dynamics over time.
Various distances are proposed and used in time-series clustering (Liao 130 ; Aghabozorgi et al. 131 ; Montero and Vilar 142 ; Mori et al. 143 ). In order to evaluate the distance between the two-time-series X T and Y T . We consider four relevant distances in time-series clustering (Leung and James 144 ). These distances represent a way to assess the similarity between the different economic time-series considered in our work.
The first distance we use is the Euclidean, derived from the Minkowski distance (Montero and Vilar 142 ): The Euclidean distance is a classical distance used in time-series clustering (Aghabozorgi et al. 131 ). However, a different approach is considered using a second distance, the Frechet one (c and Mannila 145 ). The advantage of using this distance is that we cluster the time-series considering the order of observations and the two sets of points in each row.
In this respect, start by considering:  146 , the Frechet distance can be written as: The outliers can affect the Frechet distance (Brankovic et al. 147 ), so we consider a third approach: the dynamic time warping distance (Vintsyuk 148 ; Hiroaki and Seibi 149 ; Giorgino 150 ). The dynamic time warping distance, a known approach in many different contexts, was recently considered relevant in economic applications to analyze the joint dynamics between the different time-series (Franses and Wiemann 135 ).
Liao 130 clarified that the advantage of using the Dynamic Time Warping (DTW) distance is that the algorithm can compare discrete sequences with sequences of continuous values where the two series are synchronized within DTW to align them as much as possible. So, the DTW algorithm is a generalization of traditional algorithms used to compare discrete sequences with sequences of continuous values.
As the Frechet distance, we start by minimizing the distance between combinations of observations (X a i , Y b i ). Thus, we have: Finally, as the last clustering approach, we consider the Correlation distance. We can follow Golay et al. 151 , Montero and Vilar 142 , Kim and Kim 152 , and Drago and Scozzari 153 . The Pearson's correlation distance between two time-series can be written as: where COR is the Pearson's correlation between the two considered time-series X T and Y T . The interpretation of the Correlation distance between time-series is essential: when there is a higher correlation between two timeseries, their distance becomes closer (Kim and Kim 152 ). The Correlation distance is advantageous for capturing and describing a linear pattern between different series.
Nevertheless, it can be demonstrated that the Pearson's correlation distance on clustering time-series is equivalent to the z-score normalized, squared Euclidean distance (Berthold and Höppner 154 ). This point allows higher robustness for Pearson's correlation distance.
This approach evaluates the similarity in the yearly series. The results of the approach can be interpreted as follows: a higher correlation between two time-series exists, and a lower dissimilarity between the two-timeseries can be identified simultaneously.
The different distance matrices allow assessing the similarity of each relationship (and also causal relationship) between the time-series, where we explicitly consider simulated time-series in order as a statistical benchmark. Causality relationships, both linear and nonlinear, tend to be characterized by a higher similarity in the timeseries dynamics. In economic terms, more substantial similarity is also relevant to identifying some relationships in the data that can be related by other variables acting as common determinants; yet, we expect than a higher similarity is increased by the causality.
As concerns our dataset, CO 2 is CO 2 emissions (in metric tons per capita), from the International Energy Agency (IEA) database (https:// www. iea. org/ data-and-stati stics); PCGDP is per capita GDP (in 2000 US$), from the Federal Reserve Economic Data (FRED) database (https:// fred. stlou isfed. org/); and PCEU is per capita energy use (in kg of oil equivalent), from World Bank (WB) database (https:// data. world bank. org/). To ensure the asymptotic properties, we derived the logarithmic transformations of each variable. The scatterplot matrices of the variables are given in Fig. 1.

Empirical findings
The results of several unit root and stationarity tests provided in Table 4 show that the analyzed series are nonstationary at levels, since -in general -we cannot reject the null hypothesis (H 0 ) of non-stationarity, for each series.
To check the previous results, the Lo 114 Modified Rescaled Range/Standard deviation (R/S) test and the Hurst-Mandelbrot Classical R/S test (Hurst 155 ; Mandelbrot 156 ) for long-range dependence are performed. The results are given in Table 5.
Applied to our sample, the two R/S tests fail to reject the null hypothesis of no long-range dependence at the 95% significance level for carbon dioxide emissions, whilst the other two series (energy consumption and real GDP) reject the H 0 hypothesis. Thus, there is no evidence that the emissions series is long-range dependent, while evidence of long-run dependence in the energy consumption and real GDP emerges.
To analyze the presence of structural breaks in the series the recent Ditzen et al. 115 test is applied, which implements multiple tests for structural breaks in time-series.
Following Bai and Perron 157 , this test is able to detect multiple breaks at unknown break dates. The results in Table 6 show that, when we test the first hypothesis of no break against the alternative of s = 1 break, the null is rejected (at any level). The estimated break points correspond to 1996 (oil crisis) and 2008 (world     www.nature.com/scientificreports/ economic-financial crisis). With the second hypothesis, we test the absence of breaks against a lower and upper limit of breaks (in this case, 1 ≤ s ≤ 2); again, H 0 is soundly rejected. Now, the estimated break point is 2009. Finally, the last hypothesis tests the null of s = 1 break against the alternative of one more break (s + 1 = 2); here, we cannot reject the null hypothesis. Thus, we can conclude that a single break appears in these data. To check the robustness of this result, following again the Ditzen et al. 115 approach, a test for multiple breaks at known break dates has been performed. We get a W(τ) test statistic = 13.84 (with a P-Value = 0.00); thus, the previous finding of a break in 2009 is confirmed. Since non-stationarity emerges for data at levels, we can test the (eventual) presence of a long-run relationship, or a linear combination of the series which is stationary (having a lower order of integration) (Engle and Granger 117 ). As the next step, we check for the (eventual) presence of a long-run relationship among the selected series, applying the Bayer and Hanck 116 procedure (see Table 7). The first model, which in the deterministic specification does not allow either a constant or a trend, gives a test statistic = 20.0827 (with a 5% Critical value = 10.838 and a 10% Critical Value = 8.457), based on Engle and Granger 117  In Fig. 2, the main results of the BCSG test are shown. The relationships among the variables are assessed over the time-frequency domain. Each figure displays the Wald statistics over all frequencies ω ∈ (0; π). The test statistics for the Granger non-causality from energy use to carbon emissions (Fig. 2a) are significant at the 10% level for all frequencies, while the null hypothesis of no GC is rejected at the 5% significance level for frequency in the range ω ∈ (0; 2.50). The causal flow in the reverse direction (from LCO2E to LEU) shows test statistics above the critical bounds on the whole frequency spectrum (0; 3.14), so that the H 0 hypothesis can be easily rejected at any significance level (Fig. 2b). Thus, we can conclude that a bidirectional causal flow -with a feedback mechanism -emerges as regards the energy use-CO 2 emissions nexus. Real GDP is found to cause emissions at a 5% level in the range ω ∈ (0; 0.18) and (0.51; 0.61), and at a 1% level in (0.19; 0.50); while for frequency ≥ 0.62 the null is not rejected (Fig. 2c). On the other hand, CO 2 emissions cause real GDP at least at a 5% significance level for frequencies ≤ 1.57; at a 10% level in the range ω ∈ (1.58; 1.96); then, for ω ≥ 1.97 the calculated test statistic is lower than the Critical Values (Fig. 2d). Thus, we found that the causality analyses are really sensitive to the selected frequency. Looking at the entire frequency spectrum, we can state that a unidirectional causal flow running from CO 2 emissions to real GDP exists. For the last couple of variables, real GDP is found to significantly affect energy use for frequencies ≤ 0.65 at a 5% level in the range; for frequencies in the range ω ∈ (0.76; 0.73) at a 10% level in the range; while, for ω ≥ 0.74 the calculated test statistic is lower than the Critical Values (Fig. 2e). Instead, energy use Granger causes real GDP up to ω = 0.80 at least at a 5% significance level. Therefore, we can state that for low frequencies a bidirectional causal link is discovered; however, for medium and high frequencies, the empirical evidence is in favor of the neutrality hypothesis.   www.nature.com/scientificreports/ Finally, generally speaking, the test results according to Hosoya-type conditioning are qualitatively similar. In addition, as robustness checks, we implemented unsupervised ML techniques on clusterization. The computational approach has been developed in R programming language. First, the three variables are transformed, deriving their log transformations first differences. Then, we perform the linear GC test. Finally, a nonlinear causality test is conducted.
The results for the linear Granger tests are given in Table 8. It emerges a bidirectional causal flow (feedback mechanism) between energy use and CO 2 emissions. Thus, energy use causes CO 2 emission, implying that an increase in energy use could lead to an increase in CO 2 emissions, and vice versa. These results imply that Russia was dependent on carbon energy use for its fast economic growth in the past, causing considerable CO 2 emissions. Furthermore, the "neutrality hypothesis" holds regarding the relationship between energy use and aggregate income, which states that there is no causality (in either direction) between the variables. Under the "neutrality hypothesis", the energy conservation measures do not adversely affect the economic growth path. Therefore, being these two variables mutually independent, we can state that energy consumption is not related to GDP, so that neither conservative nor expansive energy policies may have an effect on economic growth. Finally, a weak causality running from carbon emissions to real GDP is found (which is significant at a 10% level). Table 8 also reports the Granger Causality Index to quantitatively evaluate the causality nexus. Here, it is observed that the higher scores are reached for the direction of causality running from energy use to CO 2 emissions (0.75), from CO 2 emissions to energy use (0.89), and from CO 2 emissions to aggregate income (0.46).
In addition, the nonlinear GC tests are performed. The findings in Table 9 clearly clarify that none of the tested relations has a nonlinear feature. Indeed, we cannot reject the null hypothesis for each test.
The relationship between changes in CO 2 emissions and changes in energy use are well-established in the literature internationally. We tested this causal relationship for Russia, finding that they are consistent with a lot of previous studies. The relationship among energy use, CO 2 emissions, and real GDP has been empirically examined for a large variety of countries (Sohag et al. 159 ; Li and Su 160 ; He et al. 161 ). This literature showed that CO 2 emissions increase when energy use increases, mainly from fossil fuels. In the same way, a decrease in energy use can lower CO 2 emissions, positively affecting the environment. Energy production from fossil fuels is the primary source of CO 2 emissions worldwide. Therefore, considering the role of the population and the role of urbanization as well, energy use and CO 2 emissions are positively correlated (Shi 162 ; Poumanyvong and Kaneko 163 ). However, not all changes in energy use will have the same impact on CO 2 emissions. For example, if there is a shift from using fossil fuels to renewable energy sources, this may cause a CO 2 emissions reduction although in the presence of an energy use raise (Hickman et al. 164 ). On the other hand, efforts to reduce energy consumption and transition to renewable energy sources can diminish CO 2 emissions (Li and Su 160 ; Salahuddin 165 ). However, a variation in CO 2 emissions due to energy consumption can lead to a fluctuation in energy use in the mediumlong term (Hwang and Yoo 166 ). Similar considerations can be made considering the role of GDP. In fact, a CO 2 increase can follow the economic growth process (Zhang et al. 167 ). On the other hand, shocks to CO 2 series can determine the real GDP (Bozkurt and Akan 168 ; Saidi and Hammami 169 ).
Overall, the relevance of the results is twofold. Firstly, it is possible to observe an abundant literature on the bidirectional causal flow between the energy use and CO 2 emissions. This is very important because investigating the causality of the relationship is more straightforward in determining policy implications and measures. Nevertheless, our causality analyses raised a relevant point: causality tests are sensitive to the frequency domain. At the same time, it is worth noting that we considered Russia as case study, which is more relevant than ever and can have critical international implications. Table 8. Linear Granger causality tests results. P-values in parentheses. ***p < 0.01, **p < 0.05, *p < 0.10. Lag  parameter  3  3  3  3  3  3 Granger  www.nature.com/scientificreports/ As a final robustness check, let us consider four different clustering methodologies to evaluate the similarity of the time-series induced by the causality. First, it is possible to analyze if the time-series tend to be very similar and affected by common economic shocks. In the case of causality, we can explicitly identify a strong relationship between the different time-series involved. Thus, in this case, we expect to observe a more substantial similarity between the series (see Table 10).
We simulate an AR(1) process, using this statistical benchmark to evaluate the similarity between the real series and the simulated one. First, the simulated series is constructed considering the AR(1) parameter = 0.7 and subsequently transformed in the same way as the original series (taking the logarithms and the first difference). On the basis of causality findings, a more substantial similarity between energy use and carbon emissions and a weaker one between CO 2 emissions and GDP is expected. At the same time, we do not expect any similarity between the simulated time-series and the others.
A more remarkable similarity between emissions and energy consumption emerges, with a lower similarity for emissions and GDP. Finally, we found only low similarity scores between the three original variables and the simulated series. Therefore, these results soundly confirm our previous findings.
Applying the Correlation distance to the data we observe the highest similarity between energy use and carbon emissions (a lower dissimilarity expressed by the distance). This result, again, confirms the previous ones. Therefore, it is possible to affirm that the same standard temporal shocks can simultaneously fuel highly similar short-run dynamics for these series.
We can postulate the existence of a cluster of time-series that is determined by a stronger relationship between energy use and emissions because of the stronger correlations. The lower dissimilarity is reasonable given that they are simultaneously causing each other, while a weaker relationship between emissions and GDP exists.
Because of the exploratory nature of the analysis, however, the method does not formally identify the cluster. In any case, the ML analysis confirms and robustifies the time-series findings.

Conclusions and policy implications
In 2017, the Paris Climate Agreement came into force. It is aimed at implementing the United Nations Framework Convention on Climate Change and at maintaining an average global temperature growth below 2 °C. Although the agreement does not contain specific obligations for countries on GHG since the beginning of its implementation, many studies have recorded the stabilization of global CO 2 emissions deriving from the combustion of fossil fuels and industrial processes. The main practical conclusion of these studies is that stabilization and even the reduction of GHG emissions are possible without damaging economic growth. Therefore, in the current study we inspected the link among CO 2 emissions, energy use, and economic growth in Russia. In particular, the novelty of this paper is the combination of traditional time-series analyses together with the development of a new ML model. It is an important experiment because, to the best of our knowledge, in the related literature no ML experiments have been conducted for the Russian case. The econometric model appears with a test that anticipates the ML model. There is a direct relationship among the selected variables. The primary variable, in this case, is economic growth, which leads to a substantial increase in energy consumption, hence an increase of CO 2 emissions in the atmosphere. However, due to the hazardous impacts of CO 2 emissions, the strict regulations which promote the use of clean energy as opposed to fossil fuel, economic growth, and energy consumption do not seem to have a direct impact on the amount of CO 2 emissions levels. In this case, economic growth increases the consumption of energy, and therefore, the country should concentrate on producing and consuming green energy. The policy would make it easier to control carbon emissions, hence conserving the environment. In this paper, therefore, we have studied the relationship between carbon dioxide emissions, economic growth, www.nature.com/scientificreports/ and energy use through two different approaches. In the qualitative one, there emerged the existence of a direct relationship with energy consumption policies and carbon dioxide emission policies that regulate gas consumption and emissions. Besides, we have seen how economic growth and CO 2 emissions are linked to the use of coal for energy. In fact, lower economic growth could encourage the use of easily accessible and low-cost resources. On the contrary, continuous economic growth reduces the overall CO 2 emissions in terms of quality. We obtained the same results through quantitative analysis. In particular, after conducting numerous stationary tests, we have analyzed in detail the decomposition of generalized variance, and we can see a long-term relationship between our checks. However, a shock to GDP per capita affects both CO 2 emissions and energy use for some periods. This result confirms the qualitative analysis suggesting long-term structural investments capable of replacing conventional energy sources with alternative ones. In this way, CO 2 emissions will be reduced even in the presence of hypothetical shocks.
The policy implications of our analysis can be derived by combining the empirical results obtained with the analysis of emission reduction policies already initiated in Russia and, finally, the current geopolitical context.
With regard to the empirical results, in a nutshell, the work revealed a bidirectional causal flow between energy consumption and CO 2 emissions and the predominance of the "neutrality hypothesis" for the relationship between energy consumption and GDP. Strictly speaking, this means that in Russia the most exploited energy sources are fossil fuels: when energy consumption grows, supply meets this demand by increasing production from mainly fossil fuels; however, the relationship between energy consumption and GDP growth is not strictly relevant, so that GDP growth does not strictly depend on the increase in energy consumption. The final aspect to analyses is the geopolitical context. The Ukrainian-Russian conflict has created certain contextual conditions that make the future of decarbonization in Russia very complex. In particular, the restriction of trade relations between the EU and Russia has, in our view, two important implications: (1) Europe has accelerated its decarbonization process with the main objective of freeing itself from its energy dependence on Russian fossil sources, which implies a lower availability of financial resources related to the decrease in gas exports and a greater availability of fossil sources to accompany domestic industrialization processes; (2) Russia now has very limited access to import advanced technologies in the field of renewables and clean energy, technologies that are indispensable to advance decarbonization processes.
Taken together, these considerations lead to the outline of a specific policy path for Russia, which could include a mix of infrastructure upgrades and energy efficiency policies. Moreover, the levelized cost of energy (LCOE) of solar and wind is higher than that of coal in Russia, effectively requiring large subsidies to promote these new sources. Only nuclear power has an LCOE in line with coal. It should also be noted that the nonelectrified areas of the country are the most remote. In these areas there is a widespread presence of traditional generators that require hydrocarbons, the transport costs of which are very high, and consequently the LCOE of these areas is very high (Dolgushin et al. 173,174 ). It is precisely these areas that could be targeted by an intensive plan of electricity infrastructure development to reduce reliance on outdated and polluting technologies such as traditional generators, accompanied by a significant development of the electricity generation system based on nuclear and CCGT (Combined Cycle Gas Turbines), technologies that do not need to be imported. The combination of these policies could, according to our empirical analysis, lead to an increase in energy intensity with a corresponding increase in emissions. Therefore, in parallel with the empirically tested dominance of the "neutrality hypothesis" for the relationship between energy consumption and GDP, Russia should develop an energy efficiency policy involving the country's main industrial centers, again with the dual aim of improving the environmental impact of energy end-uses and promoting a national industrial chain in this sector.
The challenge of decarbonizing Russia is complicated by two structural aspects of the country's energy system: the lack of convenience in adopting RES (Renewable Energy Sources) technologies such as solar and wind power; and the lack of a national electricity grid (about two-thirds of the Russian Federation's territory, with just over 20 million inhabitants, is not electrified).
On the other hand, it should be noted that the country's non-electrified areas are the most peripheral. In these areas, the presence of traditional generators that require hydrocarbons, whose transport costs are very high, is widespread.
Furthermore, the challenge for Russia in the coming years is to develop a new strategy for the development of its energy sector, which enters a zone of high turbulence -even in the absence of the influence of the climate change agenda -due to increasing global competition, growing technological isolation, and financial constraints (Mitrova and Melnikov 174 ).
Finally, considering the current conflict between Russia and Ukraine, the rise in the price of natural resources has a potential domino effect on the world economy. The shortage of commodities, in fact, pushes up consumer prices, that is, inflation. To stem the increase in the cost of living, central banks are then forced to raise interest rates, thus reducing the amount of liquid money in circulation. Yet, the increase in interest rates usually also causes a slowdown in consumption expenditures, private investments, and the general economy, with negative www.nature.com/scientificreports/ effects on employment, which is always closely linked to the dynamics of GDP. In addition, when central banks raise interest rates, there is also an appreciation of the national currency as international investors tend to buy financial assets in those countries that offer higher interest on their government debt. This measure implies two negative effects: the increase of the imports (which causes a deterioration of the balance of payment equilibrium), and tensions on national public accounts, which may provoke a financial insolvency. Finally, the empirical results obtained were analyzed in the light of the decarbonization policy already initiated by Russia and the current economic and political context. The resulting policy implications suggest that Russia's decarbonization process could be continued through infrastructural investments in the transmission network to reduce the dependence of the country's peripheral areas on the outdated and polluting generation technologies used today, with the associated expansion of nuclear and CCGT generation capacity. At the same time, emissions could be reduced through energy efficiency processes.

Data availability
Data are available upon reasonable request to the Corresponding Author. However, raw data are also attached as Supplementary Material. www.nature.com/scientificreports/